Applications of Pattern Formation in Diffusive Instability Field on Modeling of Clod and Root System Formations

在这项工作中，寻找根系和耕作土形成的一般方面和描述是一个主要问题。该研究对从生物物理角度阐明土壤-植物系统的行为，如植物在与环境相互作用下的生长等提出了挑战，已成为植物技术领域广泛关注的问题。本研究的目的是：1)证实玉米根系和耕层结构均为分形结构。2)利用粘弹性应变场扩散失稳条件下的模式形成解释弹性材料样土裂纹的发展。3)建立基于L系统的根系分支生长模型。4)寻找根系和耕层花纹形成的控制参数。结果如下：(1)旋耕形成的重黏土土块在轮廓、裂缝、裂缝面积分布等方面均表现出幂尺度化特征，具有分形特征。此外，叶片的高频振动与土块上的裂纹间隔有关。2)玉米根系呈各向异性幂分布，呈自仿射分形。3)提出了包含弹性应变和塑性流动项的非线性耦合扩散方程来表达土的粘弹性行为，并模拟了扩散失稳条件下弹性应变的局部积累。4)玉米根系分层建模提供了一种新型的根系生长模型，突破了传统l系统方法的局限性。5)导出了土壤和根系形成的一般方面，如分形，这将为土壤-植物系统动力学研究人员提供一条途径。

Finding general aspects and descriptions of both root system and tilled clod formations is a main issue in this work. This study is a challenge to bio-physically clarifying the behavior of soil-Plant systems such as the plant growth under interactions with environment, and it has been an issue of wide interest in phytotechnology. The objectives of this work were as follows :1)to confirm that the configurations of both corn root systems and tilled clods are a kind of fractal patterns.2)to explain the development of soil cracks like elastic materials by the use of pattern formation under diffusive instability in viscoelastic strain field.3)to produce a branching growth model for a root system based upon L systems.4)to find control parameters of pattern formation on root systems and tilled clods. The results were as follows.1)Clods of heavy clay formed by rotary tillage showed power-scaling on their contours, cracks, and crack area distribution, and they were confirmed to be fractal patterns. Moreover high-frequency blade vibration was related to crack intervals on the clods.2)The root system of corn followed anisotropic power distribution like a self-affine fractal.3)Non-linear coupled diffusion equations including elastic strain and plastic flow terms were proposed for giving expression to viscoelastic behavior of soil, and local accumulation of elastic strain was simulated under diffusive instability.4)Hierarchical modeling of a corn root system provided a new type of root growth model and broke through a limit of traditional L-system methodology.5)General aspects of both clod and root system formations such as fractal were derived, and this would provide one avenue for investigators on soil-plant system-dynamics.